https://ironegg.com.cn/study/calculus/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/study/calculus/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Derivative and Differentiation"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 002 · <time datetime="2026-10-06">2026-10-06</time> · Notes </span> <h3 class="ie-document__title">Derivative and Differentiation</h3> <p class="ie-document__description">derivative 导数; differentiation 求导; product rule 乘积法则; chain rule 链式法则; implicit differentiation 隐函数求导; inverse function differentiation 反函数求导</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/study/calculus/calculus_002_differentiation.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Derivative and Differentiation">Read PDF</a> </div> </article> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Limits"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 001 · <time datetime="2026-05-23">2026-05-23</time> · Notes </span> <h3 class="ie-document__title">Limits</h3> <p class="ie-document__description">limits 极限; continuity 连续性</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/study/calculus/calculus_001_limits.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Limits">Read PDF</a> </div> </article>https://ironegg.com.cn/study/discretemathematics/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/study/discretemathematics/<p>I study physics to understand how people and firms make choices, how markets allocate resources, and how policies affect economic outcomes. This page collects my notes, diagrams, worked examples, and reflections as I connect economic models with everyday questions.</p> <h2 id="notes">Notes</h2> <p>Notes will be added as I study.</p>https://ironegg.com.cn/study/linearalgebra/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/study/linearalgebra/<p>Through MIT&rsquo;s &ldquo;Linear Algebra and NxN Systems&rdquo;, I explored foundational linear algebra, with a focus on square matrices and systems of differential equations. Studying these ideas helped me connect matrix calculations with the behavior of a system. I plan to build on this foundation through further study in mathematical modeling.</p> <p><strong>Course:</strong> </p> <h2 id="certificate">Certificate</h2> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="MITx 18.03.3x - Course Completion Certificate"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 002 · <time datetime="2026-10-08">2026-10-08</time> · Notes </span> <h3 class="ie-document__title">MITx 18.03.3x - Course Completion Certificate</h3> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/study/linearalgebra/linearalgebra-certificate.pdf" target="_blank" rel="noopener" aria-label="Read PDF: MITx 18.03.3x - Course Completion Certificate">Read PDF</a> </div> </article> <h2 id="notes">Notes</h2> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Linear Algebra - Lecture Notes"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 001 · <time datetime="2026-08-24">2026-08-24</time> · Notes </span> <h3 class="ie-document__title">Linear Algebra - Lecture Notes</h3> <p class="ie-document__description">Gaussian elimination 高斯消元法; vector spaces 向量空间; basis and dimension 基与维数; column space and nullspace 列空间与零空间; rank-nullity theorem 秩-零度定理; eigenvalues and eigenvectors 特征值与特征向量; systems of differential equations 微分方程组; coupled oscillators 耦合振子; Jacobian matrix 雅可比矩阵; stability analysis 稳定性分析; Lotka-Volterra model 洛特卡-沃尔泰拉模型; zipline modeling 滑索建模</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/study/linearalgebra/linearalgebra_001_nxnsystems.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Linear Algebra - Lecture Notes">Read PDF</a> </div> </article>https://ironegg.com.cn/modeling/mcm26/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/modeling/mcm26/<p>I and my teammates participated in the 2026 Mathematical Contest in Modeling (MCM). We chose <strong>Problem A: Modeling Smartphone Battery Drain</strong> and received <strong>Honorable Mention (H)</strong>. Our paper, <em>Making Smartphones Smarter</em>, developed an energy assumption model for smartphone applications. The project brought together mathematical modeling, numerical simulation for physical phenomena, and scientific writing within only 4 days with intensive team efforts.</p> <h2 id="problem-statement">Problem statement</h2> <p> </p> <h2 id="our-model">Our Model</h2> <p>We developed the framework in three stages: <strong>Model I - Baseline discharge:</strong> Represent the battery by a simplified Thevenin equivalent circuit and smartphone activities by power loads. <strong>Model II - Changing battery characteristics:</strong> Allow capacity, internal resistance, and open-circuit voltage to depend on temperature, cycle aging, and SOC. <strong>Model III - Thermal-electrical coupling:</strong> Add a heat-balance equation so that discharge current produces self-heating, temperature changes battery parameters, and those changes feed back into the electrical response. We compared baseline runtime predictions with published benchmarks for the iPhone 16 Pro Max and Samsung Galaxy S25 Ultra.</p> <h2 id="my-reflection">My Reflection</h2> <p>Modeling battery drain connected everyday phenomena with physics, mathematics, extensive research, and optimization. Mathematical gaps required rapid learning and AI support. Next, I&rsquo;ll study uncertainty analysis, multivariable calculus, and physics more deeply.</p> <h2 id="paper-and-certificate">Paper and Certificate</h2> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Making Smartphones Smarter - MCM 2026 Competition Paper"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 001 · <time datetime="2026-02-03">2026-02-03</time> · Notes </span> <h3 class="ie-document__title">Making Smartphones Smarter - MCM 2026 Competition Paper</h3> <p class="ie-document__description">smartphone battery drain; continuous-time modeling; equivalent circuit model; state of charge (SOC); battery aging; thermal-electrical coupling;</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/modeling/mcm26/mcm-2026-2604636.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Making Smartphones Smarter - MCM 2026 Competition Paper">Read PDF</a> </div> </article> <!-- Save your certificate beside index.md as mcm-2026-certificate.pdf. --> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="MCM 2026 - Honorable Mention Certificate"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 002 · <time datetime="2026-10-08">2026-10-08</time> · Notes </span> <h3 class="ie-document__title">MCM 2026 - Honorable Mention Certificate</h3> <p class="ie-document__description">Mathematical Contest in Modeling; Honorable Mention; smartphone battery modeling</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/modeling/mcm26/mcm-2026-certificate.pdf" target="_blank" rel="noopener" aria-label="Read PDF: MCM 2026 - Honorable Mention Certificate">Read PDF</a> </div> </article>https://ironegg.com.cn/study/microeconomics/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/study/microeconomics/<p>I study microeconomics to understand how people and firms make choices, how markets allocate resources, and how policies affect economic outcomes. This page collects my notes, diagrams, worked examples, and reflections as I connect economic models with everyday questions.</p> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Production and short-run costs"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 003 · <time datetime="2026-10-07">2026-10-07</time> · Notes </span> <h3 class="ie-document__title">Production and short-run costs</h3> <p class="ie-document__description">Marginal product, marginal cost, and average costs.</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/study/microeconomics/production-and-short-run-costs.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Production and short-run costs">Read PDF</a> </div> </article> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Price elasticity of demand"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 002 · <time datetime="2026-10-07">2026-10-07</time> · Notes </span> <h3 class="ie-document__title">Price elasticity of demand</h3> <p class="ie-document__description">The midpoint method and its relationship with revenue.</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/study/microeconomics/price-elasticity-of-demand.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Price elasticity of demand">Read PDF</a> </div> </article> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Supply, demand, and equilibrium"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 001 · <time datetime="2026-10-07">2026-10-07</time> · Notes </span> <h3 class="ie-document__title">Supply, demand, and equilibrium</h3> <p class="ie-document__description">Equilibrium calculations, curve shifts, and movements.</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/study/microeconomics/supply-demand-equilibrium.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Supply, demand, and equilibrium">Read PDF</a> </div> </article>https://ironegg.com.cn/modeling/himcm24/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/modeling/himcm24/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p>https://ironegg.com.cn/modeling/himcm25/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/modeling/himcm25/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p>https://ironegg.com.cn/modeling/himcm26/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/modeling/himcm26/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p>https://ironegg.com.cn/modeling/midmcm23/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/modeling/midmcm23/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p>https://ironegg.com.cn/study/physics/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/study/physics/<p>I study physics to understand how people and firms make choices, how markets allocate resources, and how policies affect economic outcomes. This page collects my notes, diagrams, worked examples, and reflections as I connect economic models with everyday questions.</p> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Physics01"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 001 · <time datetime="2026-10-07">2026-10-07</time> · Notes </span> <h3 class="ie-document__title">Physics01</h3> <p class="ie-document__description">Marginal product, marginal cost, and average costs.</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/study/physics/physics_notes_01.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Physics01">Read PDF</a> </div> </article>https://ironegg.com.cn/research/research1/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/research/research1/<p>I follow MIT&rsquo;s open courses to explore key derivations. Starting with single-variable calculus and progressing toward multivariable calculus, I share my notes, worked examples, and reflections on the learning way.</p> <p><strong>Courses:</strong> . . </p> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="Linear approximation"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 003 · <time datetime="2026-10-07">2026-10-07</time> · Notes </span> <h3 class="ie-document__title">Linear approximation</h3> <p class="ie-document__description">Tangent-line estimates and worked examples.</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/research/research1/linear-approximation.pdf" target="_blank" rel="noopener" aria-label="Read PDF: Linear approximation">Read PDF</a> </div> </article> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="The product rule"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 002 · <time datetime="2026-10-06">2026-10-06</time> · Notes </span> <h3 class="ie-document__title">The product rule</h3> <p class="ie-document__description">A derivation and a worked example.</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/research/research1/product-rule.pdf" target="_blank" rel="noopener" aria-label="Read PDF: The product rule">Read PDF</a> </div> </article> <style> .ie-document { box-sizing: border-box; display: flex; align-items: center; justify-content: space-between; gap: 20px; margin: 1rem 0; padding: 18px; border: 1px solid #c8d5e1; border-radius: 12px; background: linear-gradient(135deg, #f7fafc, #e8eff5); color: #334155; font-family: inherit; } .ie-document__body { min-width: 0; } .ie-document__kind { display: block; margin: 0 0 5px; color: #47667f; font-family: inherit; font-size: 12px; font-weight: 600; line-height: 1.4; } .ie-document__title { margin: 0; color: #1c3a50; font-family: inherit; font-size: 17px; font-weight: 700; line-height: 1.4; overflow-wrap: anywhere; } .ie-document__description { margin: 8px 0 0; color: inherit; font-family: inherit; font-size: 0.95rem; line-height: 1.6; overflow-wrap: anywhere; } .ie-document__actions { display: flex; flex-shrink: 0; flex-wrap: wrap; gap: 10px; margin-top: 0; } .ie-document__link { box-sizing: border-box; display: inline-flex; align-items: center; justify-content: center; min-width: 44px; min-height: 44px; padding: 10px 14px; border: 1px solid #b7cbdc; border-radius: 8px; background: #e3eef6; color: #203c51; font-family: inherit; font-size: 0.9rem; font-weight: 600; line-height: 1.3; text-align: center; text-decoration: none; } .ie-document__link--download { background: transparent; } .ie-document__link:focus-visible { outline: 2px solid #2b6cb0; outline-offset: 3px; } html.dark .ie-document { border-color: #435366; background: linear-gradient(135deg, #253647, #1c2b38); color: #dce5ec; } html.dark .ie-document__kind { color: #a9c7df; } html.dark .ie-document__title { color: #d4e7f6; } html.dark .ie-document__link { border-color: #5a7186; background: #2b4255; color: #deedf8; } html.dark .ie-document__link--download { background: transparent; } html.dark .ie-document__link:focus-visible { outline-color: #b9dbf5; } @media (max-width: 620px) { .ie-document { flex-direction: column; align-items: flex-start; gap: 0; } .ie-document__actions { margin-top: 12px; } } </style> <article class="ie-document" aria-label="The chain rule"> <div class="ie-document__body"> <span class="ie-document__kind"> No. 001 · <time datetime="2026-10-05">2026-10-05</time> · Notes </span> <h3 class="ie-document__title">The chain rule</h3> <p class="ie-document__description">The rule, its reasoning, and worked examples.</p> </div> <div class="ie-document__actions"> <a class="ie-document__link" href="https://ironegg.com.cn/research/research1/chain-rule.pdf" target="_blank" rel="noopener" aria-label="Read PDF: The chain rule">Read PDF</a> </div> </article>https://ironegg.com.cn/study/systemfunctions/Mon, 01 Jan 0001 00:00:00 +0000https://ironegg.com.cn/study/systemfunctions/<p>I study physics to understand how people and firms make choices, how markets allocate resources, and how policies affect economic outcomes. This page collects my notes, diagrams, worked examples, and reflections as I connect economic models with everyday questions.</p> <h2 id="notes">Notes</h2> <p>Notes will be added as I study.</p>